<div style="color: rgba(255, 255, 255, 0.85); font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; font-size: 16px; line-height: 24px; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;"><span style="color: #000000; font-size: 16px;">这是一套<span style="color: #000000; font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 700; font-stretch: normal; line-height: 24px; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;">53 集、系统精讲</span>的机器学习数学基础课，由<span style="color: #000000; font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 700; font-stretch: normal; line-height: 24px; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;">北大数学学院王老师</span>主讲，人民邮电出版社异步社区出品；覆盖<span style="color: #000000; font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: 700; font-stretch: normal; line-height: 24px; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;">高等数学 + 线性代数 + 概率论 + 数理统计</span>，全程手写推导、公式 step-by-step，目标是帮你扫清 ML/DL 的数学障碍。</span></div><h3 style="color: rgba(255, 255, 255, 0.85); font: 400 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;"><span style="color: #000000; font-size: 16px;">基本信息</span></h3><ul style="color: rgba(255, 255, 255, 0.85); font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; font-size: 16px; line-height: 24px; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;" class=" list-paddingleft-2"><li><p><span style="color: #000000; font-size: 16px;">集数：<span style="font: 700 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box; color: #000000;">53 集</span>（每集约 15–25 分钟）</span></p></li><li><p><span style="color: #000000; font-size: 16px;">讲师：北大数学科学学院 王老师</span></p></li><li><p><span style="color: #000000; font-size: 16px;">平台：51CTO 学堂 / 异步社区</span></p></li><li><p><span style="color: #000000; font-size: 16px;">定位：<span style="font: 700 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box; color: #000000;">够用、实用、应试 + 实战</span>，不堆砌晦涩理论</span></p></li></ul><h3 style="color: rgba(255, 255, 255, 0.85); font: 400 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;"><span style="color: #000000; font-size: 16px;">适合人群</span></h3><ul style="color: rgba(255, 255, 255, 0.85); font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; font-size: 16px; line-height: 24px; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;" class=" list-paddingleft-2"><li><p><span style="color: #000000; font-size: 16px;">想入门机器学习 / 深度学习，但<span style="font: 700 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box; color: #000000;">数学薄弱或遗忘</span>的开发者</span></p></li><li><p><span style="color: #000000; font-size: 16px;">本科修过高数 / 线代 / 概率，需要<span style="font: 700 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box; color: #000000;">系统复盘 + 定向强化</span>的学生</span></p></li><li><p><span style="color: #000000; font-size: 16px;">算法工程师 / 数据分析师，想<span style="font: 700 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box; color: #000000;">补全数学短板、夯实底层原理</span></span></p></li></ul><h3 style="color: rgba(255, 255, 255, 0.85); font: 400 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;"><span style="color: #000000; font-size: 16px;">四大模块核心内容</span></h3><h4 style="color: rgba(255, 255, 255, 0.85); font: 400 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;"><span style="color: #000000; font-size: 16px;">1. 高等数学（微积分 + 优化）</span></h4><ul style="color: rgba(255, 255, 255, 0.85); font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; font-size: 16px; line-height: 24px; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;" class=" list-paddingleft-2"><li><p><span style="color: #000000; font-size: 16px;">一元函数：极限、导数、求导法则、费马定理、泰勒展开、凸函数、极值</span></p></li><li><p><span style="color: #000000; font-size: 16px;">多元函数：偏导数、方向导数、可微、梯度、链式法则、Hessian 矩阵</span></p></li><li><p><span style="color: #000000; font-size: 16px;">优化基础：拉格朗日乘数法、KKT 条件、梯度下降 / 牛顿法原理</span></p></li></ul><h4 style="color: rgba(255, 255, 255, 0.85); font: 400 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;"><span style="color: #000000; font-size: 16px;">2. 线性代数（数据表示 + 变换）</span></h4><ul style="color: rgba(255, 255, 255, 0.85); font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; font-size: 16px; line-height: 24px; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;" class=" list-paddingleft-2"><li><p><span style="color: #000000; font-size: 16px;">向量与矩阵：运算、秩、逆、行列式、特征值 / 特征向量</span></p></li><li><p><span style="color: #000000; font-size: 16px;">空间与投影：线性空间、基、正交、投影矩阵</span></p></li><li><p><span style="color: #000000; font-size: 16px;">矩阵分解：SVD、特征分解、PCA 数学推导</span></p></li><li><p><span style="color: #000000; font-size: 16px;">矩阵求导：布局、标量 / 向量 / 矩阵互导、神经网络常用导数</span></p></li></ul><h4 style="color: rgba(255, 255, 255, 0.85); font: 400 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;"><span style="color: #000000; font-size: 16px;">3. 概率论（不确定性建模）</span></h4><ul style="color: rgba(255, 255, 255, 0.85); font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; font-size: 16px; line-height: 24px; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;" class=" list-paddingleft-2"><li><p><span style="color: #000000; font-size: 16px;">基础：随机事件、条件概率、贝叶斯定理、独立性</span></p></li><li><p><span style="color: #000000; font-size: 16px;">随机变量：分布（0-1 / 二项 / 泊松 / 正态）、期望、方差、协方差</span></p></li><li><p><span style="color: #000000; font-size: 16px;">极限定理：大数定律、中心极限定理（ML 样本估计核心）</span></p></li></ul><h4 style="color: rgba(255, 255, 255, 0.85); font: 400 16px / 24px ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; margin: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;"><span style="color: #000000; font-size: 16px;">4. 数理统计（推断 + 估计 + 检验）</span></h4><ul style="color: rgba(255, 255, 255, 0.85); font-style: normal; font-variant: normal; font-size-adjust: none; font-language-override: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-family: ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"; font-size: 16px; line-height: 24px; white-space: normal; flex: 0 1 auto; flex-direction: row; justify-content: normal; align-items: normal; padding: 0px; background-image: none; background-position: 0% 0%; background-size: auto; background-repeat: repeat; background-attachment: scroll; background-origin: padding-box; background-clip: border-box;" class=" list-paddingleft-2"><li><p><span style="color: #000000; font-size: 16px;">统计量：矩、极大似然估计（MLE）、贝叶斯估计</span></p></li><li><p><span style="color: #000000; font-size: 16px;">假设检验：显著性、p 值、置信区间</span></p></li><li><p><span style="color: #000000; font-size: 16px;">应用：回归模型参数估计、高斯混合模型（GMM）、贝叶斯分类器</span></p></li><li><p><span style="color: #000000; font-size: 16px;"><img src="https://sdtool.top/wp-content/uploads/2026/04/202604291777467907683432.png" alt="《机器学习的数学基础（53集）》，高等数学+线性代数+概率论+数理统计 mp4【2.9GB】" title="《机器学习的数学基础（53集）》，高等数学+线性代数+概率论+数理统计 mp4【2.9GB】" /></span></p></li></ul><p><span style="color: #000000; font-size: 16px;"><br/></span></p><p><span style="color: #000000; font-size: 16px;"></span></p><p><span style="color: #000000; font-size: 16px;"><img src="https://sdtool.top/wp-content/uploads/2026/04/202604291777467776824375.png" alt="《机器学习的数学基础（53集）》，高等数学+线性代数+概率论+数理统计 mp4【2.9GB】（2）" title="《机器学习的数学基础（53集）》，高等数学+线性代数+概率论+数理统计 mp4【2.9GB】（2）" /></span></p>
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